Southern Republican leaders yesterday urged Congress and the Reagan administration to press for an extension of the Voting Rights Act of 1965, and to expand its coverage beyond the South to the entire nation.

The southern party leaders, in Washington for a meeting of the Republican National Committee, also made it clear that they will not give a "free ride" in 1982 congressional elections to conservative Democrats who vote for Ronald Reagan's economic program.

Reagan upset many GOP leaders last week by saying he could not "find it in my conscience" to campaign against Democrats who support his economic program. Most of these are conservative southerners, known as "boll weevils."

White House chief of staff James A. Baker III reiterated Reagan's position in a luncheon speech, saying: "The best politics is the passage of the president's economic recovery program. The best politics is a strong president going into the 1982 election."

Party leaders avoided putting themselves publicly at odds with the president, who hosted RNC members at White House reception. But southerners made it clear they have their own agendas to pursue.

"Regardless of what the president wants to do, my job is to elect Republicans," said Texas GOP chairman Chet Upham Jr. in a remarked echoed by other party leaders. "The number one vote in Congress as far as I'm concerned is the first one, electing the speaker. So I'll be looking at every conservative Democrat seat with the idea of picking up a Republican one."

The White House has tried to keep Reagan out of the debate over the Voting Rights Act, considered the mose effective civil rights bill ever passed. At the request of national party Chairman Richard Richards, no formal resolution was presented at the southern caucus to avoid an anticipated fight before the entire RNC on the emotional issue.

The gentlemen's agreement on the matter, however, put party leaders at odds with several of the region's most prominent Republicans, including Senate Judiciary Chairman Strom Thurmond (R-S.C.). Thurmond, who opposed the act when it first passed, has said he wants either to eliminate provisions requiring states covered by the law to get prior federal approval for any changes in their voting laws, or make the section applicable to all states.

The southern party officials, however, endorsed the "pre-clearance" provisions of the law. Nine states -- all in the South -- and portions of 13 others are covered by pre-clearance provisions. Many southern politicians argue that the provisions discriminate against their region.

Southern GOP leaders hope their agreement will pacify these critics, and at the same time avoid putting the GOP leaders in the positions of appearing to be against blacks and other minorities that the party is trying to attract.

"A lot of us think the Voting Rights Act wasn't all that bad," said Mississippi national committeeman Clark Reed. "We've lived with it 16 years, and a lot of good came out of it."

This week is the first time Gop leaders from around the country have gathered since Reagan's inauguration, and the mood was almost euphoric. The party war chest, they were told in one breath, is almost overflowing: Unlike the financially pinched Democrats, the RNC has $9 million in the bank.

In the next breath, party finance chairman Richard DeVos told them he was putting the muscle on every member of the committee, senators, congressmen, Reagan and Vice President Bush to give at least $25 to become sustaining members of the party.